{
  "abstract": "In a Hamiltonian lattice gauge theory, the physical Hilbert space is fixed by the Gauss law, by choosing an eigenspace of the Gauss law operator which generates the gauge transformation. Choosing a non-trivial eigenspace is referred to as the modified Gauss law. In 2+1d dynamical U(1) pure gauge theory, we show that these physical Hilbert spaces are defect Hilbert spaces associated with non-topological monodromy defects for monopole operators and topological defects for U(1) 1-form symmetry, inserted along the time direction. We also construct the corresponding lattice translation operators. Under a nontrivially modified Gauss law, these translations obey a magnetic translation algebra. Finally, we discuss how the modified Gauss laws are manifested in 2+1d compact bosons, via exact duality on the lattice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11417",
  "author_total": 2,
  "authors": [
    {
      "name": "Pengcheng Wei"
    },
    {
      "name": "Yunqin Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/308kg9wbmsf1r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11417",
  "fulltext_url": null,
  "id": "308kg9wbmsf1r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11417",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.str-el"
    ],
    [
      "arxiv",
      "hep-th"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.11417",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/308kg9wbmsf1r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:26Z",
      "native_id": "2609.11417",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11417"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.str-el",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    }
  ],
  "title": "Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality",
  "title_text": "Gauss Law, Monodromy Defect, Magnetic Lattice Translation, and Lattice Duality",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:26Z",
  "url": "https://research.draconitic.com/paper/308kg9wbmsf1r",
  "venue": "arXiv",
  "versions": []
}